Find the sum of the geometric series with a1 = 243, r = -2/3, And n = 5

Answer: Sum of 5 terms of give geometric series is 165. Solution: Need to find the sum of geometric series.  Given that  First term of geometric series [tex]a_{1}[/tex] = 243 Common ratio of geometric series r = [tex]\frac{-2}{3}[/tex]Number of terms in series = n = 5 Sum of geometric series when r < 1 is given by following formula [tex]s=\frac{a_{1}\left(1-r^{n}\right)}{1-r}[/tex][tex]\frac{243\left(1-\left(-\frac{2}{3}\right)^{5})\right.}{1-\left(\frac{-2}{3}\right)}[/tex][tex]\frac{243\left(1-\left(\frac{-32}{243}\right)\right)}{1+\frac{2}{3}}[/tex][tex]\frac{\frac{243(243+32)}{243}}{\frac{5}{3}}[/tex] = 55 x 3 = 165  Hence sum of 5 terms of give geometric series is 165.